Calculating the gravitational acceleration

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SUMMARY

When calculating gravitational acceleration between two objects of comparable mass, it is essential to compute the acceleration for both masses rather than assuming one is fixed. The fundamental principle of F = ma applies only in an inertial frame, meaning both objects must be considered in the calculation. This approach ensures accurate results, especially when neither mass is significantly larger than the other. General relativity is not a factor in this context, simplifying the calculations to Newtonian mechanics.

PREREQUISITES
  • Understanding of Newton's laws of motion, specifically F = ma
  • Basic knowledge of gravitational force and acceleration
  • Familiarity with inertial frames of reference
  • Concepts of mass and gravitational interaction
NEXT STEPS
  • Study the implications of Newton's laws in non-inertial frames
  • Explore gravitational interactions in multi-body systems
  • Learn about the principles of general relativity and its differences from Newtonian mechanics
  • Investigate practical applications of gravitational calculations in astrophysics
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding gravitational interactions between objects of comparable mass.

wrongusername
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When calculating the gravitational acceleration between two objects of comparable mass, should I find the acceleration caused by gravity for both masses and then add the accelerations togeether, or should I just find the acceleration for one of the masses? I was thinking that since there's a gravitational force acting on both objects, I should find the accelerations caused by gravity for both objects before getting the acceleration of the objects towards each other.
 
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wrongusername said:
When calculating the gravitational acceleration between two objects of comparable mass … I was thinking that since there's a gravitational force acting on both objects, I should find the accelerations caused by gravity for both objects before getting the acceleration of the objects towards each other.

Hi wrongusername! :wink:

Yes. :smile:

The essential principle is that (unless you're working in general relativity, which I'm assuming you're not) F = ma etc only works in an inertial frame.

So you can't calculate on the basis that one body is fixed (unless of course it's sooo much heavier than the other, eg the Earth and you, that it's as good as fixed).

Calculate each acceleration from the point of view of a fixed observer, and proceed from there. :wink:
 
tiny-tim said:
Hi wrongusername! :wink:

Yes. :smile:

The essential principle is that (unless you're working in general relativity, which I'm assuming you're not) F = ma etc only works in an inertial frame.

So you can't calculate on the basis that one body is fixed (unless of course it's sooo much heavier than the other, eg the Earth and you, that it's as good as fixed).

Calculate each acceleration from the point of view of a fixed observer, and proceed from there. :wink:

Thank you for the explanation! :smile:
 

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